B"H
At the beginning of parshas Vayeira, Rashi says that Hashem came to Avraham to "visit the sick" on the third day after the bris.
And [the Lord] appeared to him: to visit the sick (Tan. Buber, Vayera 1). Said Rabbi Chama the son of Chanina: It was the third day from his circumcision, and the Holy One, blessed be He, came and inquired about his welfare (B. M. 86b).
Why did Hashem wait all the way into the third day to visit him? Why not on the first day?
It could be like the maharal explains that on the 3rd day you're the most sick. On the first day it's a wound which needs to heal. Your body is trying to heal it, so on the 3rd day he felt the weakest.
Answer already given, but this Or HaChaim gives a fuller discussion:
An additional meaning of the verse and the way it is phrased is that G'd appeared to Abraham for Abraham's sake. The Torah here alludes to something discussed in Baba Metzia 86. Rabbi Chama son of Chanina stated that this vision occurred on the third day after the circumcision. G'd came and enquired after Abraham's wellbeing. How did Rabbi Chama know that it was the third day? If we were to deduce this from Genesis 34,25, where we are told that the third day after the people of Shechem had circumsised themselves was a day they experienced additional pains, this cannot be, because we have a definitive statement in Shabbat 134 that the first and second day after the circumcision are more dangerous to the patient! True, the Talmud there distinguishes between the pain and the relative healing process experienced by adults (pain lasts longer, healing occurs more slowly), compared to that experienced by minors. However, such a distinction applies only to the third day, not to the first two days. On the first two days everyone experiences the most pain.
Besides, do not use the fact that Shimon and Levi did not attack the people of Shechem until the third day after their circumcision as an argument. These sons of Jacob were not concerned with the pain of the people of Shechem but with their physical weakness, their relative inability to offer resistance. The third day is definitely the day such patients feel weakest. Regarding the danger of infection from the wound and danger to life, etc., the first two days are far more dangerous than the third day. Why should we assume then that G'd did not come and visit Abraham on the first or second day after the circumcision? I have found an interesting comment in the Tur Yore Deah item 335 in which he quotes this folio in the Talmud without mentioning that it was on the third day. According to that version the simple message of Rabbi Chama is that G'd came to pay a visit to the sick. [The discussion in Shabbat 134 concerns washing a baby with hot water on the third day after the circumcision if the third day is on the Sabbath; permission to do this indicates that on that day the baby's life is in danger. Ed.]
He also explains why Hashem might not have visited Avraham on the first day:
According to the opinion of Ran that the first and the third days are the most dangerous to the patient, whereas the second day is not sufficiently dangerous to desecrate the Sabbath, we can understand the matter better. When you do not feel in danger, G'd applies the general rule of not visiting the sick during the first three hours of the morning. On the first day one also does not visit the sick as we know from Nedarim 40. When Rava was sick, he told his household not to tell anyone on the first day about his being sick in order not to influence his horoscope negatively. Rashi explains this to mean "that one should not talk about the sick person." [As long as the matter is not public knowledge an immediate cure may result without the debits and merits of the sick person being reviewed in heaven because of people talking about him. Ed.] However Rava did want the fact that he was sick publicised from the second day on, so that all those who hated him should rejoice over his being sick. This would help diminish his debits [in the accounts kept in the celestial ledger. Ed.]. Rabbi Chama did not think G'd visited on the first day, as such a visit would certainly not have gone unnoticed, and as a result tongues would have been set wagging. Yerushalmi Peah third chapter states that the relatives of a sick person may visit him immediately; this is because such visits do not contribute to the sickness of the patient becoming public knowledge. There is certainly no doubt that G'd Himself must be viewed as a very close relative of the sick person. However, a visit by G'd would most certainly attract attention. According to the opinion that there is no difference in the degree of danger on either of the respective three days, this would leave the question of why Rabbi Chama had to mention the third day as the day G'd visited Abraham. We may have to assume that these people had the version of the Tur which did not mention the third day at all.
I will note a couple of interesting points:
The Gemara notes: And in stating this, Rav disagrees with that statement of Rabbi Ḥama, son of Rabbi Ḥanina. As Rabbi Ḥama, son of Rabbi Ḥanina, says, and likewise the school of Rabbi Yishmael taught: In reward for three acts of hospitality that Abraham performed for the angels, his descendants merited three rewards. The Gemara elaborates: In reward for providing them with curd and milk, the Jewish people merited the manna; in reward for: “And he stood [omed] by them,” the Jews merited the pillar [amud] of cloud; in reward for Abraham saying: “Let now a little water be fetched,” they merited the well of Miriam. This statement does not distinguish between actions performed by Abraham himself and those performed by means of a messenger.
Shlomy quoting Maharal is correct. But it isn't just the Maharal who says it but the Torah explicitly.
After Dinah was raped Jacob's 2 sons attacked on the third day after their circumcision when they were the most sore. Bereishit 34:25
3rd day is apparently when you are the most sore the Torah tells us
